TY - JOUR
T1 - Learning structures of Bayesian networks for variable groups
AU - Parviainen, Pekka
AU - Kaski, Samuel
PY - 2017
Y1 - 2017
N2 - Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to represent different “views” to or aspects of the same entities, one may be more interested in modeling dependencies between groups of variables rather than between individual variables. Motivated by this, we study prospects of representing relationships between variable groups using Bayesian network structures. We show that for dependency structures between groups to be expressible exactly, the data have to satisfy the so-called groupwise faithfulness assumption. We also show that one cannot learn causal relations between groups using only groupwise conditional independencies, but also variable-wise relations are needed. Additionally, we present algorithms for finding the groupwise dependency structures.
AB - Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to represent different “views” to or aspects of the same entities, one may be more interested in modeling dependencies between groups of variables rather than between individual variables. Motivated by this, we study prospects of representing relationships between variable groups using Bayesian network structures. We show that for dependency structures between groups to be expressible exactly, the data have to satisfy the so-called groupwise faithfulness assumption. We also show that one cannot learn causal relations between groups using only groupwise conditional independencies, but also variable-wise relations are needed. Additionally, we present algorithms for finding the groupwise dependency structures.
KW - Bayesian networks
KW - Conditional independence
KW - Multi-view learning
KW - Structure learning
UR - http://www.scopus.com/inward/record.url?scp=85020309004&partnerID=8YFLogxK
UR - https://arxiv.org/abs/1508.07753
U2 - 10.1016/j.ijar.2017.05.006
DO - 10.1016/j.ijar.2017.05.006
M3 - Article
AN - SCOPUS:85020309004
VL - 88
SP - 110
EP - 127
JO - INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
JF - INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
SN - 0888-613X
ER -